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Research Papers

On the Comprehensive Kinematics Analysis of a Humanoid Parallel Ankle Mechanism

[+] Author and Article Information
Chengxu Zhou

Humanoid and Human Centered Mechatronics
Research Line,
Istituto Italiano di Tecnologia,
via Morego, 30,
Genova 16163, Italy
e-mail: zhouchengxu@gmail.com

Nikos Tsagarakis

Humanoid and Human Centered Mechatronics
Research Line,
Istituto Italiano di Tecnologia,
via Morego, 30,
Genova 16163, Italy
e-mail: nikos.tsagarakis@iit.it

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 23, 2017; final manuscript received June 25, 2018; published online August 6, 2018. Assoc. Editor: Pierre M. Larochelle.

J. Mechanisms Robotics 10(5), 051015 (Aug 06, 2018) (7 pages) Paper No: JMR-17-1358; doi: 10.1115/1.4040886 History: Received October 23, 2017; Revised June 25, 2018

In this paper, we present a thorough kinematics analysis of a humanoid two degrees-of-freedom (DoF) ankle module based on a parallel kinematics mechanism. Compared with the conventional serial configuration, the parallel kinematics ankle permits the distribution of the torque/power of the actuators to the two DoF of the ankle taking full advantage of available power/torque capacity of the two actuators. However, it complicates the kinematics study in return. In this work, a complete study of a parallel ankle mechanism is performed that permits the full characterization of the ankle module for the purpose of its design study, control, and performance evaluation. Screw theory is employed for mobility analysis to first determine the number and properties of the mechanism's DoFs. Then the inverse kinematics is solved analytically and the Jacobian matrix for describing the velocity relation between the ankle joints and motors is found. Based on these results, the forward kinematics of the parallel mechanism can be numerically computed using the Newton–Raphson method. The workspace of the ankle is also analyzed and the motor limits are decided accordingly. Finally, an experimental demonstration consisting of four tests is carried out to evaluate the proposed methods and ankle module.

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Figures

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Fig. 1

Mechanical model of the CogIMon humanoid robot (left) and close back view of its tibia without covers (right)

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Fig. 2

The ankle's schematic representation

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Fig. 3

Typical Control Framework for humanoid motion control. The superscript m indicates the variable is measured by the sensors.

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Fig. 4

The ankle workspaces with respect to only the mechanism geometry, are illustrated in green for the default equal dimensions, in blue by increasing the motor bar length, in pink by increasing the rod length and in yellow by increasing the spacing between the two rods, respectively

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Fig. 5

The workspace of the proposed ankle illustrated by different motor limits with the lower limit varying from −90 to −60 deg and the upper limit varying from 90 to 40 deg. The red box represents the desired workspace. Therefore, the minimum required motor limits are [−64, 50] degree.

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Fig. 6

Ankle joint references for the four experimental tests

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Fig. 7

Motor references solved by inverse kinematics for the four experimental tests

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Fig. 8

Roll and pitch angle errors between the input references and the resultant ones after the IK-FK computation

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Fig. 9

Number of iterations for solving the forward kinematics during experiment

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Fig. 10

Computational time of inverse and forward kinematics during experiment

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Fig. 11

Snapshots of the four experimental tests5

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